*> \brief \b ZHB2ST_KERNELS * * @precisions fortran z -> s d c * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZHB2ST_KERNELS + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZHB2ST_KERNELS( UPLO, WANTZ, TTYPE, * ST, ED, SWEEP, N, NB, IB, * A, LDA, V, TAU, LDVT, WORK) * * IMPLICIT NONE * * .. Scalar Arguments .. * CHARACTER UPLO * LOGICAL WANTZ * INTEGER TTYPE, ST, ED, SWEEP, N, NB, IB, LDA, LDVT * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), V( * ), * TAU( * ), WORK( * ) * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHB2ST_KERNELS is an internal routine used by the ZHETRD_HB2ST *> subroutine. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> \endverbatim *> *> \param[in] WANTZ *> \verbatim *> WANTZ is LOGICAL which indicate if Eigenvalue are requested or both *> Eigenvalue/Eigenvectors. *> \endverbatim *> *> \param[in] TTYPE *> \verbatim *> TTYPE is INTEGER *> \endverbatim *> *> \param[in] ST *> \verbatim *> ST is INTEGER *> internal parameter for indices. *> \endverbatim *> *> \param[in] ED *> \verbatim *> ED is INTEGER *> internal parameter for indices. *> \endverbatim *> *> \param[in] SWEEP *> \verbatim *> SWEEP is INTEGER *> internal parameter for indices. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER. The order of the matrix A. *> \endverbatim *> *> \param[in] NB *> \verbatim *> NB is INTEGER. The size of the band. *> \endverbatim *> *> \param[in] IB *> \verbatim *> IB is INTEGER. *> \endverbatim *> *> \param[in, out] A *> \verbatim *> A is COMPLEX*16 array. A pointer to the matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER. The leading dimension of the matrix A. *> \endverbatim *> *> \param[out] V *> \verbatim *> V is COMPLEX*16 array, dimension 2*n if eigenvalues only are *> requested or to be queried for vectors. *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (2*n). *> The scalar factors of the Householder reflectors are stored *> in this array. *> \endverbatim *> *> \param[in] LDVT *> \verbatim *> LDVT is INTEGER. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array. Workspace of size nb. *> \endverbatim *> *> \par Further Details: * ===================== *> *> \verbatim *> *> Implemented by Azzam Haidar. *> *> All details are available on technical report, SC11, SC13 papers. *> *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra. *> Parallel reduction to condensed forms for symmetric eigenvalue problems *> using aggregated fine-grained and memory-aware kernels. In Proceedings *> of 2011 International Conference for High Performance Computing, *> Networking, Storage and Analysis (SC '11), New York, NY, USA, *> Article 8 , 11 pages. *> http://doi.acm.org/10.1145/2063384.2063394 *> *> A. Haidar, J. Kurzak, P. Luszczek, 2013. *> An improved parallel singular value algorithm and its implementation *> for multicore hardware, In Proceedings of 2013 International Conference *> for High Performance Computing, Networking, Storage and Analysis (SC '13). *> Denver, Colorado, USA, 2013. *> Article 90, 12 pages. *> http://doi.acm.org/10.1145/2503210.2503292 *> *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra. *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure *> calculations based on fine-grained memory aware tasks. *> International Journal of High Performance Computing Applications. *> Volume 28 Issue 2, Pages 196-209, May 2014. *> http://hpc.sagepub.com/content/28/2/196 *> *> \endverbatim *> * ===================================================================== SUBROUTINE ZHB2ST_KERNELS( UPLO, WANTZ, TTYPE, $ ST, ED, SWEEP, N, NB, IB, $ A, LDA, V, TAU, LDVT, WORK) * IMPLICIT NONE * * -- LAPACK computational routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. CHARACTER UPLO LOGICAL WANTZ INTEGER TTYPE, ST, ED, SWEEP, N, NB, IB, LDA, LDVT * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), V( * ), $ TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), $ ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER I, J1, J2, LM, LN, VPOS, TAUPOS, $ DPOS, OFDPOS, AJETER COMPLEX*16 CTMP * .. * .. External Subroutines .. EXTERNAL ZLARFG, ZLARFX, ZLARFY * .. * .. Intrinsic Functions .. INTRINSIC DCONJG, MOD * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. * .. Executable Statements .. * AJETER = IB + LDVT UPPER = LSAME( UPLO, 'U' ) IF( UPPER ) THEN DPOS = 2 * NB + 1 OFDPOS = 2 * NB ELSE DPOS = 1 OFDPOS = 2 ENDIF * * Upper case * IF( UPPER ) THEN * IF( WANTZ ) THEN VPOS = MOD( SWEEP-1, 2 ) * N + ST TAUPOS = MOD( SWEEP-1, 2 ) * N + ST ELSE VPOS = MOD( SWEEP-1, 2 ) * N + ST TAUPOS = MOD( SWEEP-1, 2 ) * N + ST ENDIF * IF( TTYPE.EQ.1 ) THEN LM = ED - ST + 1 * V( VPOS ) = ONE DO 10 I = 1, LM-1 V( VPOS+I ) = DCONJG( A( OFDPOS-I, ST+I ) ) A( OFDPOS-I, ST+I ) = ZERO 10 CONTINUE CTMP = DCONJG( A( OFDPOS, ST ) ) CALL ZLARFG( LM, CTMP, V( VPOS+1 ), 1, $ TAU( TAUPOS ) ) A( OFDPOS, ST ) = CTMP * LM = ED - ST + 1 CALL ZLARFY( UPLO, LM, V( VPOS ), 1, $ DCONJG( TAU( TAUPOS ) ), $ A( DPOS, ST ), LDA-1, WORK) ENDIF * IF( TTYPE.EQ.3 ) THEN * LM = ED - ST + 1 CALL ZLARFY( UPLO, LM, V( VPOS ), 1, $ DCONJG( TAU( TAUPOS ) ), $ A( DPOS, ST ), LDA-1, WORK) ENDIF * IF( TTYPE.EQ.2 ) THEN J1 = ED+1 J2 = MIN( ED+NB, N ) LN = ED-ST+1 LM = J2-J1+1 IF( LM.GT.0) THEN CALL ZLARFX( 'Left', LN, LM, V( VPOS ), $ DCONJG( TAU( TAUPOS ) ), $ A( DPOS-NB, J1 ), LDA-1, WORK) * IF( WANTZ ) THEN VPOS = MOD( SWEEP-1, 2 ) * N + J1 TAUPOS = MOD( SWEEP-1, 2 ) * N + J1 ELSE VPOS = MOD( SWEEP-1, 2 ) * N + J1 TAUPOS = MOD( SWEEP-1, 2 ) * N + J1 ENDIF * V( VPOS ) = ONE DO 30 I = 1, LM-1 V( VPOS+I ) = $ DCONJG( A( DPOS-NB-I, J1+I ) ) A( DPOS-NB-I, J1+I ) = ZERO 30 CONTINUE CTMP = DCONJG( A( DPOS-NB, J1 ) ) CALL ZLARFG( LM, CTMP, V( VPOS+1 ), 1, TAU( TAUPOS ) ) A( DPOS-NB, J1 ) = CTMP * CALL ZLARFX( 'Right', LN-1, LM, V( VPOS ), $ TAU( TAUPOS ), $ A( DPOS-NB+1, J1 ), LDA-1, WORK) ENDIF ENDIF * * Lower case * ELSE * IF( WANTZ ) THEN VPOS = MOD( SWEEP-1, 2 ) * N + ST TAUPOS = MOD( SWEEP-1, 2 ) * N + ST ELSE VPOS = MOD( SWEEP-1, 2 ) * N + ST TAUPOS = MOD( SWEEP-1, 2 ) * N + ST ENDIF * IF( TTYPE.EQ.1 ) THEN LM = ED - ST + 1 * V( VPOS ) = ONE DO 20 I = 1, LM-1 V( VPOS+I ) = A( OFDPOS+I, ST-1 ) A( OFDPOS+I, ST-1 ) = ZERO 20 CONTINUE CALL ZLARFG( LM, A( OFDPOS, ST-1 ), V( VPOS+1 ), 1, $ TAU( TAUPOS ) ) * LM = ED - ST + 1 * CALL ZLARFY( UPLO, LM, V( VPOS ), 1, $ DCONJG( TAU( TAUPOS ) ), $ A( DPOS, ST ), LDA-1, WORK) ENDIF * IF( TTYPE.EQ.3 ) THEN LM = ED - ST + 1 * CALL ZLARFY( UPLO, LM, V( VPOS ), 1, $ DCONJG( TAU( TAUPOS ) ), $ A( DPOS, ST ), LDA-1, WORK) ENDIF * IF( TTYPE.EQ.2 ) THEN J1 = ED+1 J2 = MIN( ED+NB, N ) LN = ED-ST+1 LM = J2-J1+1 * IF( LM.GT.0) THEN CALL ZLARFX( 'Right', LM, LN, V( VPOS ), $ TAU( TAUPOS ), A( DPOS+NB, ST ), $ LDA-1, WORK) * IF( WANTZ ) THEN VPOS = MOD( SWEEP-1, 2 ) * N + J1 TAUPOS = MOD( SWEEP-1, 2 ) * N + J1 ELSE VPOS = MOD( SWEEP-1, 2 ) * N + J1 TAUPOS = MOD( SWEEP-1, 2 ) * N + J1 ENDIF * V( VPOS ) = ONE DO 40 I = 1, LM-1 V( VPOS+I ) = A( DPOS+NB+I, ST ) A( DPOS+NB+I, ST ) = ZERO 40 CONTINUE CALL ZLARFG( LM, A( DPOS+NB, ST ), V( VPOS+1 ), 1, $ TAU( TAUPOS ) ) * CALL ZLARFX( 'Left', LM, LN-1, V( VPOS ), $ DCONJG( TAU( TAUPOS ) ), $ A( DPOS+NB-1, ST+1 ), LDA-1, WORK) ENDIF ENDIF ENDIF * RETURN * * END OF ZHB2ST_KERNELS * END